Answer:
Part a) [tex]AB=17\ m[/tex]
Part b) [tex]AC=20.8\ m[/tex]
Step-by-step explanation:
see the attached figure with letters to better understand the problem
Part a) Find the length AB
Applying the Pythagoras Theorem in the right triangle ABH
[tex]AB^2=AH^2+HB^2[/tex]
where
AB is the hypotenuse (the greater side)
AH and HB are the legs of the right triangle
we have
[tex]AH=FG=8\ m[/tex]
[tex]HB=GB-ED=26-11=15\ m[/tex]
substitute the values
[tex]AB^2=8^2+15^2[/tex]
[tex]AB^2=289[/tex]
[tex]AB=17\ m[/tex]
Part a) Find the length AC
Applying the Pythagoras Theorem in the right triangle ABC
[tex]AC^2=AB^2+BC^2[/tex]
where
AC is the hypotenuse (the greater side)
AB and BC are the legs of the right triangle
we have
[tex]BC=12\ m[/tex]
[tex]AB=17\ m[/tex]
substitute
[tex]AC^2=17^2+12^2[/tex]
[tex]AC^2=433[/tex]
[tex]AC=20.8\ m[/tex]
